Other mistake: At the end, before House's "realisation" the camera pans out and shows a street light when House and Wilson are outside talking. The lamp top is covered with fresh snow. It's been dark for sometime. The heat from the bulb would have melted snow had it actually been real.
Continuity mistake: A third of the way into the show when Hadley and House are arguing while walking out of House's office, Hadley's necklace watch is backwards and out of the top of her blouse. When they stop walking and switched to a shot of House then back to Hadley, her necklace watch is right-side front and inside the top of her blouse.